I recently revisited this question and it occurred to me that in the general push to identify a similar-sounding (or similar-looking) word that in a foreign language means something like "important [thing or person]," we may not have given enough consideration to a simpler explanation: the possibility (which poster Been There has attempted in three separate answers to champion) that the phrase originally referred to an extremely large cheese. With the aim of taking that possibility seriously, I offer the following investigation into the history of big cheese and main cheese.
'Big cheese' as a magnet for public attention
Although Been There's supporting documentation focuses on 1,230-pound cheese presented to Thomas Jefferson in 1802 following his election as U.S. president, the production of gigantic cheeses for display at fairs and other public exhibitions is a recurring theme during the nineteenth century. Such exhibitions became increasingly common over the second half of that century.
An Elephind search for "big cheese" yields the following decade-by-decade progression in number of newspaper matches: 1830s, 2, 1840s, 1; 1850s, 13; 1860s, 45; 1870s, 72, 1880s, 75; 1890s, 174. Many of these matches involve references to a large but by no means enormous cheese, and others are fragments of longer phrases such as "a big [as in major] cheese manufacturer." But others, across the years, refer to mammoth cheeses that were created for display. Here are some examples.
From "One Day Later in Washington," in the Rutland [Vermont] Herald (February 28, 1837):
Mr Alford opposed the motion for a recess. He said it was time, if they intended to do any public business this session, that they forthwith set about it, for they had wasted time enough already. As for the battle with the great cheese at the White House [which had been delivered there in honor of the departing President Andrew Jackson], he was for leaving it to those whose taste led them there, and tomorrow they might receive a full account of the killed and slain. ...
Mr Wise remarked that it was pretty well understood where the absent members had gone. There was a big cheese to be eaten at the White House to-day, and the appetites of members had driven them to partake in the treat.
From an untitled item in the [Pittsburgh, Pennsylvania] Daily Morning Post (April 26, 1848):
The editor of the Nashville [Tennessee] Union speaks of a cheese in that city, as "the largest cheese we have ever seen;" and he says:—"It is said to weigh 700 pounds, and is unquestionably the daddy of all the little cheeses!" It is no doubt true, that this is the biggest cheese that our Nashville friend has ever seen; but the rest of his statement is not to be taken for granted. He has surely forgotten about that big cheese, presented to the revered patriot of the Hermitage [Andrew Jackson], which was cut when Mr. Van Buren was inaugurated, and weighed 1400 pounds! Why your Nashville cheese is only one of the great grand children of that; for there were various others sent to Washington at the same time, that were about the same size of yours!
From an untitled item in the Gallipolis [Ohio] Journal (April 27, 1854):
Ford & Drouillard "cut a big cheese" the other day, and submitted a large slice to our judgment. Well, it is good and no mistake, if you don't believe it, "pitch in" and taste for yourself.
From an untitled item in the Greencastle [Indiana] Banner (October 27, 1864):
The Californians are famous for big mines, big trees, etc., and now have added a big cheese to their list of big brags. At the late Sanitary Fair in San Francisco, a cheese weighing 3,800 pounds net, manufactured by Steele & Brother, of Pescadora [probably Pescadero], was on exhibition in the Floral Temple. The Messrs. Steele removed to California from Lorain county, Ohio, a number of years ago. and engaged in the vicinity of San Francisco. How successfully, their monster cheese shows.
From an item in the [Santa Rosa, California] Sonoma Democrat (May 27, 1876):
A Big Cheese
An Ohio dairyman proposes to make a cheese for the Centennial to weigh 25,000 pounds. It will require one day’s milk from 20,000 cows and will be as much cheese as 50,000 men can comfortably eat in one day. It would feed all the citizens of Santa Rosa for about two weeks and there would be scraps enough left to bait all the rat-traps in the State.
From "Mammoth Cheeses," in the [Chicago, Illinois] Prairie Farmer (October 10, 1885):
One of the traditions in the dairy region of Central New York is that of the big cheese made there and sent to Andrew Jackson by his admirers, when he was President of the United States [1829–1837]. It was a formidable undertaking in those days to make a cheese weighing 800 lbs, and its successful accomplishment showed much enterprise. But with the present system of associated dairying a cheese four times as large as the historic article of 50 years ago, is made without serious difficulty. ...
Two others still larger [than 3,000 pounds] were recently made to order of Mr. Geo. W. Hayward, an enterprising dealer of Buffalo, N.Y. who had already distinguished himself in this direction. One of his cheeses was made on Tuesday, Sept. 22, and the second two days later. The first weighed 3,306 lbs, and the second 3,340 lbs. They are to be cut up and sold respectively for Thanksgiving and Christmas. To stimulate the sale, Mr. Hayward dropped ten gold coins of $5 each in the curd, while it was being placed in the mammoth hoop. ... The only advantage claimed for these monster cheeses is novelty.
From "Topics of the Day," in The Washington [D.C.] Critic (April 7, 1888), recounting the story of the great cheese given to Thomas Jefferson in 1802:
The cheese was put to press with prayer and hymn-singing and great solemnity. When it was well dried it weighed 1,600 pounds. It was placed on a sleigh, and Elder John Leland drove with it all the way [from Cheshire, Massachusetts] to Washington. It was a journey of three weeks. All the country had heard of the big cheese, and came out to look at it as the elder drove along.
From "The Great Exposition: Some of the Spectacular Features of the World's Fair," in the Wichita [Kansas] Daily Eagle (February 22, 1893):
In the agricultural section is to be a mammoth among commonplace displays. It is a cheese—a plain Canadian cheese, but its weight is 26,000 pounds, its height six feet and its diameter nine feet. It furnishes so much weight within a small area that the foundation of the floor had to be strengthened to sustain it.
Kansas shows the variety of the country's forest monstrosities in a section of a walnut log 9 feet in diameter and so heavy that, like the big cheese, it has to have a special foundation in the Forestry building.
From "When We Were Boys: A Picture of an Old-time Celebration in the Country," originally printed in the Boston Post, reprinted in the [Monmouth, Illinois] Warren County Democrat (June 28, 1894), evidently describing a celebration of the Fourth of July in a typical Massachusetts village sometime in the 1850s:
By 10 o'clock all the town was out [for the Independence Day celebration], and so many from the country that the village contained 3,000 or 4,000 people. If the season had been very early "down on the sand barrens," a few watermelons were fr sale, but not often. Of home-made beer, ginger cakes, currant pies, striped candy and the like, the sale was wonderful—a stand under every big tree. In the village grocery the big cheese [not previously mentioned in this article] was cut and regular customers invited to taste it. "Cuba six" cigars (six for 5 cents) were so plentiful that every boy could have one.
From "Davis County Cheese," in the Salt Lake [City, Utah] Herald (July 4, 1897):
The Hooper Dairy company has made the big cheese for the manufacturer's float [for the Independence Day parade]. It is about the size of a wagon wheel and 14 inches in depth, weighing about 700 pounds.
As these various examples indicate, big cheeses were a crowd-pleasing attraction at major holidays and exhibitions in nineteenth- and early twentieth-century America—not unlike butter cow sculptures today. Given that history, it is not unthinkable that people of a sarcastic turn of mind might have noticed an unfamiliar politician or other celebrity surrounded by admirers in a public place and asked, "Who is the big cheese?"—without any intention of invoking a word from Urdu, Farsi, French, German, Italian, or Ukrainian that sounds more or less similar to cheese.
Earliest instances of 'big cheese' as a person who is the center of attention
The earliest instance of big cheese in arguably its modern figurative sense actually involves an extended metaphor of "big cheese" and "little cheese." From "Those Cotton Associations," in the [Dallas, Texas] Southern Mercury and Farmers Union Password (February 1, 1906):
Col. E. S. Peters of Calvert served with distinguished honors for a number of years as "the Texas Cotton Growers' Protective Association." The Colonel was just about "the whole cheese."
But to be exact, there were two cheeses—E.S. Peters, who was "President," and R.E. Smith, who figured acceptably as "Vice-President." As this astute pair comprided the entire lay membership, as well as the full corps of officers of the Texas Cotton Growers' Protective Association, it was as harmonious an agricultural organization as the world has ever known. Did serious differences ever arise between State presidents and vice-presidents as to which should play "second fiddle"? you ask. Probably not. The plan of each State president selecting his own "man Friday," his own second, assured harmony among them. The little cheese dared not fall out with the big cheese, you know.
The usage seems to have caught on more generally in 1908–1909. From "Calls Roosevelt 'the Big Cheese'" in the Spokane [Washington] Press (September 18, 1908):
In commenting on the recent convention that nominated [Charles Evans] Hughes for reelection under pressure from [Theodore] Roosevelt, "Fingey" Conners, the New York democratic state chairman, delivered himself of the following political classic:
"Wot's the use of those guys going to Saratoga, anyway? Why, no use at all. Every one knew that the candidate had been selected by the big cheese at Oyster Bay [Roosevelt's home town]. At Saratoga it was just the same as it was at Chicago. Oyster Bay did the whole t'ing."
From "'David and Goliath' by [Billy] Sunday: Well Known Evangelist Gives His Version of the Famous Conflict — Says David Soaked Goliath on the Coco between the Lamps," in the Wenatchee [Washington] Daily World (January 8, 1909):
"In the morning old Goliath comes out in front of the Philistines and dares the Israelites to fight him. 'Who's that big stiff making all the big talk out there?' asks Dave.
"'Why, that's the big cheese, the big noise,' says his brothers.
"'Why don't some one soak him one?' asks Dave.
"'We've all got cold feet,' says the Israelites.
From "Later Cohan Show Falls Below Standard Set by Earlier Show," in the Washington [D.C.] Times (March 30, 1909):
About "Forty-Five Minutes From Broadway" is a quiet retreat, much to the old homestead with a happy forever after effect. Here the Kid [Burns] hies himself after a busy session of public life and hits it up with the muse while he loosens his half-Nelson on grammar. Nothing doing on the quiet life. The villainess heads the procession in a repentant mood and returns the certified check. A honeymoon pair halts to pay their respects to Burns, then comes the big cheese in [millionaire Dudley] Wilcox him himself. Father has gotten wise to the Kid's little act of self-sacrifice and the whole unqualified family is ready to fall on his shoulders, even unto both parties of the second generation.
From "About A.P. Walker's Jerseys," in Chicago [Illinois] Livestock World (May 28, 1909):
When we all get down to A.P. Walker's new home at Rushville, Ind., to attend his Jersey [cow] sale on June 16, the "big cheese" will be Derry's Golden Jolly. His sister sold for $3,860 two years ago and a daughter for $2,500.
And from an untitled item in the [Mesquite] Texas Mesquiter (September 10, 1909):
Gov. Campbell finds that he cannot be at El Paso to meet Presidents Taft and Diaz, but informs the committee that he will visit El Paso later. Perhaps the Governor prefers to go when he can be the Big Cheese.
That's five instances in less than a full year, from New York, Washington state, Washington D.C., Illinois, and Texas—quite a distribution. I briefly investigated the possibility that big cheese might be related to big wheel (as in "big wheel of cheese"), but it appears from a much earlier instance of big wheel (from the [Santa Rosa, California] Sonoma Democrat, January 27, 1872) that the latter term refers to gear wheels:
The [San Francisco] Fire Department was to have been called out [for a parade review] on the same afternoon, but the Fire Commissioners, thinking they had not been treated with sufficient consideration, refused to permit it.
The fact that the Mayor could not order them out in spite of the Commissioners, was a source of more astonishment to the Prime Minister of Japan, than the display could possibly have been. Their [the Japanese delegation's] first idea of the machinery of government is a big wheel which turns all the other wheels. As it was, they learned more than they could have done by the parade.
'Main cheese' as a slang term for 'important person'
The phrase main cheese is far less common than big cheese in Elephind search results, with only 12 matches from the entire nineteenth century and 32 more from the first decade of the twentieth century, many of which do not use it as a set phrase. Nevertheless, several of the matches do use main cheese as a slang term, supplementing the early Google Books instances cited above.
From "Coming Attractions," in the Los Angeles [California] Herald (December 24, 1899):
George Fuller Golden, that Titian haired humorist, whose quaint quips and gay stories of his redoubtable friend Casey amused Orpheum audiences so mightily last year, is again to the front, and as of yore, he tops an Orpheum bill. He is the piece de resistance of the new bill, which in Irish is equivalent to "main cheese." Golden has that wonderful gift of being able to magnetize an audience and with no other aids than a brilliant smile, a shock of auburn hair and a vast fund of very funny stories and an occasional song with an imitation or two thrown in for good measure, Golden convulses his hearers and sets the rafters ringing with the echoes of the laughing people.
From a series of humorous one-off items in the Houston [Texas] Post (October 13, 1901):
Instead of being the main cheese in after dinner oratory, Chauncey will soon play the part of large and enthusiastic audience at a course of after bedtime curtain lectures.
From "One Forty-two," in the Wichita [Kansas] Daily Eagle (November 3, 1901):
"Me an' T'ree Twenty-seven goes against de night school game an' gits wise dat what we needs better ventilation. Dat bad air stops up de pores on' puts a kid on de bum. We makes a spiel to de Main Cheese dat we got to have a electric fan to keep de gray matter cool out in de waitin room. He takes it up wid de Board of Directors and dey pass a appropriation of two sixty-t'ree to make de great reform. ..."
"We has a bank roll wid six eighteen in it, when one day de Main Cheese—dat's de manager—goes against de wheel an' drops two twenty-six.Dat makes him sore, an' so he makes a order dat gamblin is de curse of de nation, an' we got to pay back all de dough dat we won. ..."
This sense of main cheese persists through the middle 1920s and then becomes quite rare, although Elephind does offer this example from "Super Sunday Is Just Not What It Used to Be," in the [Pennsylvania State] Collegian (January 24, 1990):
The 49er's have everything going for them. They have dismantled each of their playoff opponents and are playing like a "dynasty" team. No team has repeated as the NFL's main cheese since the Steelers did it in '79 and '80.
'Whole cheese' as a slang term for 'important person'
Another expression with a brief vogue (particularly between 1898 and 1910) in the United States as a slang term meaning "big shot" is whole cheese. The first instance that Elephind turn up is from an untitled item in the [Dallas, Texas] Southern Mercury (July 7, 1898):
The Democrats are having a hot time in Pennsylvania. Harrity has his war clothes and is determined to prove to Jim Jones that Jim Guffy is not the whole cheese in that State. The fight is a bitter one, and the aureate statesman has decided to give Guffy the "hottest shot he has in the shop."
From "As Other Towns See It," in the Rock Island [Illinois] Argus (July 18, 1898):
Says the Ottumwa Courier: "And the Rock Island paper is not the only one that is talking that way now. Down in Quincy, where they thought Sidney Frick was the whole cheese, they are beginning to realize the fact that a [baseball] club run by a board of home directors is much [better] for a town than if the club is turned over to one man absolutely.
From an untitled item in the Wichita [Kansas] Daily Eagle (September 7, 1898):
Chaplain McIntyre, who said that the Oregon at the battle of Santiago was the whole cheese, will be court-martialed. Such a declaration tended to disorganize Admiral Sampson's peace of mind.
From "Ward Conventions: Republicans Name Candidates for Justices and Constables," in the Salt Lake [City, Utah] Herald (September 23, 1898):
Bonetti, who had been appointed sergeant-at-arms, was fain to cry, "Ladies and gentlemen, behave yourselves," which they did, and after a discussion, a motion, two amendments and an amendment to the amendment to the amendment, offered by Joe Cottle, who was apparently the whole cheese, a collection was taken up and $10.35 raised which was confided to the car of Mr Post who placed the amount down in the deepest pocket he he had and took a station near the door, where he could readily escape.
About two dozen more instances of whole cheese in the sense of the most important person or thing appear in Elephind search results between this last instance and December 24, 1899, when the first instance of main cheese appears with the same meaning.
Three different poplar slang phrases with cheese-related themes debut within a fairly brief span of years in Elephind newspaper database search results. In July 1898, we see the first match for whole cheese (or more precisely, the whole cheese), a term that continues to appear in newspaper matches until 1944, despite peaking between 1900 and 1920. In December 1899, we get the first Elephind match for main cheese in very nearly the same sense; that expression—far less popular than whole cheese—peaked in the first decade of the twentieth century and died out (except for a couple of outliers much later) in 1944 as well. Big cheese made its Elephind debut as a slang term for "important person" in February 1906 and continues to be in use to this day.
The nineteenth-century history of "the big cheese" as a very large cheese that commanded popular attention and appeared especially at special events and on special occasion certainly provides a plausible basis for the term big cheese to come into use as a slang term applied to an important person—but to get there, we have to go through whole cheese and main cheese, which (in the newspaper data that I have access to) predate the personified big cheese by, respectively, seven years and six years.
That's a not insignificant problem—but I feel far more inclined today to take large cheeses seriously as the ultimate referent source of big cheese in the slang sense than I did four years ago.